Theoretically for something to have negative rest mass must mean it has negative rest energy.

E0=M0*v^2

Therefore when rest mass of M0 < 0, any value for velocity v squared is greater than or equal to 0, since √ -1 = i where i ≠ ℝ.

Anyway, negative mass means in my mind that the mass dimension is negative, thus when affected by gravity (if it would be), since F = ma and F = mg when free-falling under gravity, it would have negative acceleration (deceleration) or negative force (or positive relative to direction). Gravity would seemingly repel rather than absorb the object to the centre of the object.